A Novel Foward-PDE Approach as an Alternative to Empirical Mode Decomposition

TL;DR

This paper introduces a forward heat equation model as a theoretical alternative to empirical mode decomposition, improving understanding, robustness, and performance in signal processing tasks.

Contribution

The paper presents a novel PDE-based model for EMD, offering a theoretical foundation and enhanced performance over classical methods.

Findings

Better handling of mode-mixing signals

More robust to noise compared to classical EMD

Provides a mathematical basis for EMD analysis

Abstract

In this paper we present a mathematical model of the Empirical Mode Decomposition (EMD). Although EMD is a powerful tool for signal processing, the algorithm itself lacks an appropriate theoretical basis. The interpolation and iteration processes involved in the EMD method have been obstacles for mathematical modelling. Here, we propose a novel forward heat equation approach to represent the mean envelope and sifting process. This new model can provide a better mathematical analysis of classical EMD as well as identifying its limitations. Our approach achieves a better performance for a "mode-mixing" signal as compared to the classical EMD approach and is more robust to noise. Furthermore, we discuss the ability of EMD to separate signals and possible improvements by adjusting parameters.